On Jun 19, 5:48 am, Richard Fateman <fate... at cs.berkeley.edu> wrote:
> Perhaps you wanted
>
> SetPrecision [1.000000000000000000000001, 60] -1
>
> which returns..
>
> 9.9999999999999863800355333982586279*10^-25
>
> This takes the binary software-float number that
> is closest to 1.000...1 accurate to the equivalent of about 24 deci=
mal
> digits. Then extends it on the right by
> appending additional binary zeros to it until it gets to the binary
> precision which is the equivalent of about 60 decimal digits.
> Then subtracts exactly 1, which happens to be an exact number
> in binary float.
>
> WRI claims their arithmetic is intuitive and easy to understand
> and does the right thing almost all the time.
The arithmetic is reasonably intuitive. The user interface is less so.
>
> On the other hand, you are not the first person to be puzzled by it.
Approximation is often puzzling. The ideological war you wage against
WRI is unhelpful here. The wise person understands that there are
multiple points of view. Your IEEE754-based ideology has its own
weaknesses: abuse of the concepts of "rational" and "finite", and weak
connection to the real number system. Matthew 7:3 applies.